中文摘要：

记[k]={1,2,…,k）,称为颜色集.设φ：E（G）→[k]为图G的边集合到[k]的映射,令f（v）表示与顶点v关联的边的颜色的加和.如果对任意一条边uv∈E（G）,都有φ（u）≠φ（v）,f（u）≠f（v）,则称φ为图G的邻和可区别[k]-边染色,k的最小值称为图G的邻和可区别边色数,记为ndi_Σ（G）.若对任意一条边uv∈E（G）,都有f（u）≠f（v）,则称φ为图G的k-边权点染色,称图G是k-边权可染的.运用组合零点定理证明了对于最大度不等于4的Halin图有：ndi_∑（G）≤Δ（G）＋2,并证明了任一Halin图是4-边权可染的.

英文摘要：

Let [k] = {1,2,...,k}, it is the color set. Let φ ： E（G） →[k] be a mapping. Let f（v） denote the sum of the colors of the edges incident with vertex v. ~ is called a neighbor sum distinguishing [k]- edge coloring of G ifφ（u） ≠φ（v）, f（u） ≠ f（v） for each edge uv C E（G）. The smallest value k in such a coloring of G is called neighbor sum distinguishing edge index, and is denoted by ndi∑（G）. ~ is called a vertex coloring k- edge weighting of G if f（u） ≠ f（v） for each edge uv E E（G）. G is called k- edge weight colorable. By using the Combinatorial Nullstellensatz, it is proved that ndi∑（G） ≤A（G） ＋ 2 for each Halin graph with A（G）≠ 4, and each Halin graph is 4-edge weight colorable.